This article proposes an unequivocal method of labeling and numbering the cladding modes propagating in single-mode opticalwaveguides with tilted periodic structures. The unambiguous determination of individual propagating modes in this type of optical fiber is crucial for their use in sensory systems. The selection of the appropriate spectral range and mode determines the sensitivity and measuring range of tilted fiber Bragg grating (TFBG) sensors. The measurement methods proposed by individual research teams using TFBGs as transducers are usually based on the selection of specific modes. Unification of the labeling of modes and their numbering enables comparison of the basic metrological parameters of individual measurement methods and reproduction and verification of the proposed sensors and methods in the laboratories of other scientific and research centers.

In this article, we study tilted fiber Bragg gratings (TFBGs) with tilt angles of 6◦ and 8◦, their transmission spectra, and spectral parameters that have a linear dependence on the refractive index of the environment. It is shown that there can be several such characteristics, such as the minimum, width and energy of the spectrum. The linear dependence of the spectrum width on the refractive index does not depend on the tilt angle. The linear dependence of the spectrum minimum is only observed for a tilt angle of 8◦. The results of this work can be used to create a sensor system based on an optical fiber.

The article presents an analysis of the impact of bending optical fibers with tilted Bragg gratings on their spectral parameters. This article proves that it is possible to a choose TFBG cladding mode and the optical spectrum range related to it that allows the best metrological properties to be obtained when measuring bend. The results contained in the paper explain why the minima in the spectral characteristics, corresponding only to some cladding modes, change their shape during TFBG bending, which is important for application of Bragg gratings as bending sensors. It has been presented that in the case of TFBG we are able to aggregate the knowledge obtained during experiment to the form of a physical model of the fiber bending sensor.